On the asymptotic expansions of various quantum invariants II: the colored Jones polynomial of twist knots at the root of unity $e^{\frac{2\pi \sqrt{-1}}{N+\frac{1}{M}}}$ and $e^{\frac{2\pi \sqrt{-1}}{N}}$

Qingtao Chen, Shengmao Zhu

This is the second article in a series devoted to the study of the asymptotic expansions of various quantum invariants related to the twist knots. In this article, following the me…